Random Forest

Kristen Monaco, Praya Cheekapara, Raymond Fleming, Teng Ma

Random Forest Introduction

  • Ensemble machine learning method based on a large number of decision trees voting to predict a classification
  • Benefits compared to decision tree:
    • Able to function with incomplete data
    • Lower likelihood of an overfit
    • Improved prediction accuracy

Random Forest Applications

  • Regression
    • Price Prediction
    • Demand Forecasting
    • Time-series Analysis

  • Remote Sensing
    • Vegetation Mapping
    • Environmental Monitoring
  • Bioinformatics
    • Disease Diagnosis
    • Protein Classification
    • Gene Expression

  • Banking and Business
    • Fraud Detection
    • Targeted Marketing

Methods

  • Bagging
  • Boosting
  • Random Feature Selection
  • Cross Validation

Common Improvements

  • Bootstrap Sampling (Bagging)
    • Each decision tree uses a random sample of the original dataset
      • Using a subset of the dataset reduces the probability of an overfit model
      • Rows with missing data will often be left out of the sample, improving performance
      • Performed with replacement
  • Boosting
    • When individual models are trained in a sequential way, each model then learns the mistakes made by preceding model.

Random Feature Selection

  • A random set of features is selected for each node in training
    • Information about feature importance may be saved and applies in future iterations
    • Even with automated random feature selection, feature selection and engineering prior to training may improve performance

Decision Tree and Cross Validation

  • Validation of performance of model
    • Resampling method similar to out of bag estimation
    • Allows estimation of the general performance of a model
  • Single decision trees may be visualized to help modelers understand the dataset

Code 
 m3 <- rpart(
   formula = Group~ LF + GF + Biomes + Range +
     Habitat_degradation + Habitat_loss + IAS +
     Other + Unknown + Other + Over_exploitation,
   data    = species_train,
   method  = "anova"
 )
 rpart.plot(m3)

Dataset and Exploration

  • South African Red List
    • Data about plants with their habitat, traits, distribution, and factors influencing their current threatened/extinct status
  • Purpose
    • Predict whether or not an unknown plant is threatened based on the above characteristics

Distribution of Range by Conservation Status

  • While there are a small number of threatened species with a large range, it is clear that Range is likely a strong predictor of Group status

  • A lower range predicts a higher likelihood of threatened or extinct grouping.

Code 
ggplot(data = data, aes(x = Status, y = Range, fill = Status)) +
  geom_boxplot() +
  theme_bw() +
  ylim(0,100000)

Feature Associations

  • Cramer’s V Association with Range binned into 20 categories
    • Target feature Group is most associated with Range, Family, Habitat Loss, Biome, and GF
    • The most associated features will likely be the most important features during model training
    • Colinearity does not appear to be present, further checks are

Code 
corrDF <- train %>% mutate(Range=ntile(Range, n=20))
corrDF %<>% mutate_at(c("Group","LF","GF","Biomes","Range","Habitat_degradation","Habitat_loss",
                        "IAS","Other","Over_exploitation","Pollution","Unknown"),factor)
corrDF <- corrDF %>% mutate(Range=ntile(Range, n=20))
corrplot::corrplot(DescTools::PairApply(corrDF,DescTools::CramerV), type='lower')

Data Preparation

  • Preprocessing
    • Encode categorical features into numerical / factor features
    • Split the training set into a training and test set, minimizing class imbalance

Class Balancing

  • Class Imbalance
    • Resample smaller classes in order to approximate equal classes
    • Training on imbalanced datasets will bias predictions to the larger class
Group Counts Pre-Balancing:   490 148 23 
Group Counts Post-Balancing:  490 490 490
data_train_AB <- data_train
data_train_AB <- data_train_AB[data_train_AB$label 
                      != '3',]
data_train_AB_resampled <- ovun.sample(label ~ .,
                      data = data_train_AB, method = "over", 
                      N = 980, seed = 1)$data

data_train_AC <- data_train
data_train_AC <- data_train_AC[data_train_AC$label
                      != '2',]
data_train_AC_resampled <- ovun.sample(label ~ .,
                      data = data_train_AC,
                      method = "over", N = 980,
                      seed = 1)$data

data_train_AB_2 <- data_train_AB_resampled[data_train_AB_resampled$label
                      == '2',]
data_train_AC_3 <- data_train_AC_resampled[data_train_AC_resampled$label
                      == '3',]

data_train_1 <- data_train_AB_resampled[data_train_AB_resampled$label 
                      == '1',]
data_train_combined <- rbind(data_train_1, data_train_AB_2, data_train_AC_3)

cat("Group Counts Pre-Balancing:  ",table(data_train$label),
        "\nGroup Counts Post-Balancing: ",table(data_train_combined$label))

Model Training

\(X_{new}=\frac{X_{old}-\min(X_{old})}{\max(X_{old})-\min(x_{old})}\)

          Score
Accuracy   0.88
Recall     0.79
Precision  0.82
F1         0.81
features_train_1 <- as.data.frame(lapply(features_train, 
                      function(x) {(x-min(x))/(max(x)-min(x))}))
features_test_1 <- as.data.frame(lapply(features_test, 
                      function(x) {(x-min(x))/(max(x)-min(x))}))

data_train_1 <- features_train_1
data_train_1$label <- label
class_counts_1 <- table(data_train_1$label)

model_1 <- randomForest(x = data_train_1[-ncol(data_train_combined)],
                        y = as.factor(data_train_1$label), ntree = 2)
variable_importance_1 = importance(model_1)
pred_comb_1 <- predict(model_1, features_test_1)
accuracy <- sum(label_test == pred_comb_1) / length(label_test)
label_test_factor <- as.factor(label_test)
pred_comb_1_factor <- as.factor(pred_comb_1)
cm <- confusionMatrix(pred_comb_1_factor, label_test_factor)
recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"], 
                 cm$byClass["Class: 2", "Sensitivity"], 
                 cm$byClass["Class: 3", "Sensitivity"]))
precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"], 
                    cm$byClass["Class: 2", "Pos Pred Value"], 
                    cm$byClass["Class: 3", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                  ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall',
                       'Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}-\bar{X}_{old}}{\sigma_{X_{old}}}\)

          Score
Accuracy   0.40
Recall     0.53
Precision  0.41
F1         0.46
features_train_2 <- as.data.frame(lapply(features_train, 
                      function(x) {(x - mean(x))/sd(x)}))
features_test_2 <- as.data.frame(lapply(features_test, 
                      function(x) {(x - mean(x))/sd(x)}))

data_train_2 <- features_train_2
data_train_2$label <- label
class_counts_2 <- table(data_train_2$label)

model_2 <- randomForest(x = data_train_2[-ncol(data_train_combined)],
                      y = as.factor(data_train_2$label), ntree = 2)
variable_importance_2 = importance(model_2)
pred_comb_2 <- predict(model_2, features_test_2)
accuracy <- sum(label_test == pred_comb_2) / length(label_test)
label_test_factor <- as.factor(label_test)
pred_comb_1_factor <- as.factor(pred_comb_2)
cm <- confusionMatrix(pred_comb_1_factor, label_test_factor)
recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                              cm$byClass["Class: 2", "Sensitivity"],
                              cm$byClass["Class: 3", "Sensitivity"]))

precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                            cm$byClass["Class: 2", "Pos Pred Value"],
                            cm$byClass["Class: 3", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                  ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}}{\max(|X_{old}|)}\)

          Score
Accuracy   0.88
Recall     0.71
Precision  0.79
F1         0.75
features_train_3 <- as.data.frame(lapply(features_train, 
                       function(x) {x / max(abs(x))}))
features_test_3 <- as.data.frame(lapply(features_test, 
                        function(x) {x / max(abs(x))}))

data_train_3 <- features_train_3
data_train_3$label <- label
class_counts_3 <- table(data_train_3$label)

model_3 <- randomForest(x = data_train_3[-ncol(data_train_combined)], 
                        y = as.factor(data_train_3$label), 
                        ntree = 2)
variable_importance_3 = importance(model_3)
pred_comb_3 <- predict(model_3, features_test_3)
accuracy <- sum(label_test == pred_comb_3) / length(label_test)
label_test_factor <- as.factor(label_test)
pred_comb_1_factor <- as.factor(pred_comb_3)
cm <- confusionMatrix(pred_comb_1_factor, label_test_factor)
recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                 cm$byClass["Class: 2", "Sensitivity"],
                 cm$byClass["Class: 3", "Sensitivity"]))
precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                 cm$byClass["Class: 2", "Pos Pred Value"],
                 cm$byClass["Class: 3", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                  ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}-\min(X_{old})}{\max(X_{old})-\min(x_{old})}\)

          Score
Accuracy   0.77
Recall     0.57
Precision  0.54
F1         0.56
features_train_4 <- as.data.frame(lapply(features_train, 
                       function(x) {x / sum(abs(x))}))
features_test_4 <- as.data.frame(lapply(features_test, 
                       function(x) {x / sum(abs(x))}))

data_train_4 <- features_train_4
data_train_4$label <- label
class_counts_4 <- table(data_train_4$label)

model_4 <- randomForest(x = data_train_4[-ncol(data_train_combined)], 
                        y = as.factor(data_train_4$label), ntree = 2)
variable_importance_4 = importance(model_4)
pred_comb_4 <- predict(model_4, features_test_4)
accuracy <- sum(label_test == pred_comb_4) / length(label_test)
label_test_factor <- as.factor(label_test)
pred_comb_1_factor <- as.factor(pred_comb_4)
cm <- confusionMatrix(pred_comb_1_factor, label_test_factor)
recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                              cm$byClass["Class: 2", "Sensitivity"],
                              cm$byClass["Class: 3", "Sensitivity"]))
precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                            cm$byClass["Class: 2", "Pos Pred Value"],
                            cm$byClass["Class: 3", "Pos Pred Value"]))
F1 = 2 * recall * precision / ( recall + precision )
printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),
                    ncol=1,byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')
print(printTable)

\(X_{new}=\frac{X_{old}-\bar{X}_{old}}{\sigma_{X_{old}}}\)

          Score
Accuracy   0.75
Recall     0.43
Precision  0.49
F1         0.46
features_train_5 <- as.data.frame(lapply(features_train, 
                       function(x) {x / sqrt(sum(x^2))}))
features_test_5 <- as.data.frame(lapply(features_test, 
                       function(x) {x / sqrt(sum(x^2))}))

data_train_5 <- features_train_5
data_train_5$label <- label
class_counts_5 <- table(data_train_5$label)

model_5 <- randomForest(x = data_train_5[-ncol(data_train_combined)], 
                        y = as.factor(data_train_5$label), ntree = 2)
variable_importance_5 = importance(model_5)
pred_comb_5 <- predict(model_5, features_test_5)
accuracy <- sum(label_test == pred_comb_5) / length(label_test)
label_test_factor <- as.factor(label_test)
pred_comb_1_factor <- as.factor(pred_comb_5)
cm <- confusionMatrix(pred_comb_1_factor, label_test_factor)

recall <- mean(c(cm$byClass["Class: 1", "Sensitivity"],
                 cm$byClass["Class: 2", "Sensitivity"],
                 cm$byClass["Class: 3", "Sensitivity"]))

precision <- mean(c(cm$byClass["Class: 1", "Pos Pred Value"],
                 cm$byClass["Class: 2", "Pos Pred Value"],
                 cm$byClass["Class: 3", "Pos Pred Value"]))

F1 = 2 * recall * precision / ( recall + precision )

printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),ncol=1,
                    byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')

print(printTable)

Prediction Method

  • Each independently trained decision tree produces its own prediction
    • Trained on different subsets of both data and features
  • The results from each decision tree are combined into a voting classifier using a Mode function
    • \(y_{final}=\text{mode}(\{y_1,y_2,y_3,y_4,y_5\})\)
  • Iterate over entire test set, storing results
  • Generate a confusion matrix, calculate the sensitivity, and precision for each category

Prediction

          Score
Accuracy   0.92
Recall     0.89
Precision  0.93
F1         0.91
  • Prediction using a combination of trees leads to a better accuracy on all metrics
n <- length(pred_comb_1)

final_pred <- rep(NA, n)

for(i in 1:n) {
   preds <- c(pred_comb_1[i], pred_comb_2[i], pred_comb_3[i], 
              pred_comb_4[i], pred_comb_5[i])

   final_pred[i] <- as.numeric(names(which.max(table(preds))))
}

importances_list <- list(variable_importance_1, variable_importance_2, 
                         variable_importance_3, variable_importance_4, 
                         variable_importance_5)
average_importance <- Reduce("+", importances_list) / 
                      length(importances_list)


accuracy <- sum(label_test == final_pred) / length(label_test)


final_pred_factor <- as.factor(final_pred)
label_test_factor <- as.factor(label_test)

cm_vote <- confusionMatrix(final_pred_factor, label_test_factor)

sensitivity_class1 <- cm_vote$byClass["Class: 1", "Sensitivity"]
sensitivity_class2 <- cm_vote$byClass["Class: 2", "Sensitivity"]
sensitivity_class3 <- cm_vote$byClass["Class: 3", "Sensitivity"]
recall = (sensitivity_class1 + sensitivity_class2 + sensitivity_class3)/3


precision_class1 <- cm_vote$byClass["Class: 1", "Pos Pred Value"]
precision_class2 <- cm_vote$byClass["Class: 2", "Pos Pred Value"]
precision_class3 <- cm_vote$byClass["Class: 3", "Pos Pred Value"]
precision = (precision_class1 + precision_class2 + precision_class3)/3


F1 = 2 * recall * precision / ( recall + precision )


printTable=matrix(c(round(accuracy,2),round(recall,2),
                    round(precision,2),round(F1,2)),ncol=1,
                    byrow=TRUE)
colnames(printTable)=c('Score')
rownames(printTable)=c('Accuracy','Recall','Precision','F1')

print(printTable)

Feature Importance

  • Range is the most important feature to predict Group Status
    • Habitat Loss and Growth Form are also important features
    • Life Form, Other, and Unknown are unimportant for prediction
ctrl <- trainControl(method = "cv",  
                     number = 10) 

bagged_cv <- train(
  Group~ LF + GF + Biomes + Range +
    Habitat_degradation + 
    Habitat_loss + IAS + Other +
    Unknown + Other +
    Over_exploitation,
  data    = species_train,
  method = "treebag",
  trControl = ctrl,
  importance = TRUE
)
 
plot(varImp(bagged_cv), 10)

Evaluation

\(\text{Accuracy}=\frac{\sum{\left(\text{Actual Label} = \text{Predicted Label}\right)}}{\text{Label Count}}\)

\(\text{Recall}\quad \;=\frac{\text{True Positives}}{\text{True Positives} + \text{False Negatives}}\)

\(\text{Precision}=\frac{\text{True Positives}}{\text{True Positives}+\text{False Positives}}\)

\(\text{F1}\qquad \;=\frac{2*(\text{Precision}*\text{Recall})}{\text{Precision}+\text{Recall}}\)

Confusion Matrix and Statistics

Confusion Matrix and Statistics

          Reference
Prediction   1   2   3
         1 200  12   1
         2  10  51   0
         3   0   0   9

Overall Statistics
                                          
               Accuracy : 0.9187          
                 95% CI : (0.8805, 0.9478)
    No Information Rate : 0.742           
    P-Value [Acc > NIR] : 3.035e-14       
                                          
                  Kappa : 0.7929          
                                          
 Mcnemar's Test P-Value : NA              

Statistics by Class:

                     Class: 1 Class: 2 Class: 3
Sensitivity            0.9524   0.8095  0.90000
Specificity            0.8219   0.9545  1.00000
Pos Pred Value         0.9390   0.8361  1.00000
Neg Pred Value         0.8571   0.9459  0.99635
Prevalence             0.7420   0.2226  0.03534
Detection Rate         0.7067   0.1802  0.03180
Detection Prevalence   0.7527   0.2155  0.03180
Balanced Accuracy      0.8871   0.8820  0.95000

Code 
cm_vote <- confusionMatrix(final_pred_factor, label_test_factor)
 
cm <- confusionMatrix(final_pred_factor, label_test_factor)
cm
 
cm_d <- as.data.frame(cm$table)
cm_st <-data.frame(cm$overall)
cm_st$cm.overall <- round(cm_st$cm.overall,2)
cm_d$diag <- cm_d$Prediction == cm_d$Reference
cm_d$ndiag <- cm_d$Prediction != cm_d$Reference     
cm_d[cm_d == 0] <- NA
cm_d$Reference <-  reverse.levels(cm_d$Reference)
cm_d$ref_freq <- cm_d$Freq * ifelse(is.na(cm_d$diag),-1,1) 
 
plt1 <-  ggplot(data = cm_d, aes(x = Prediction , y =  Reference, 
                                 fill = Freq))+
  scale_x_discrete(position = "top") +
  geom_tile( data = cm_d,aes(fill = ref_freq)) +
  scale_fill_gradient2(guide = FALSE ,low="red",high="mediumvioletred", 
                       mid= "mistyrose",
                    midpoint = 0,na.value = 'white') +
  geom_text(aes(label = Freq), color = 'black', size = 3)+
  theme_bw() +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        legend.position = "none",
        panel.border = element_blank(),
        plot.background = element_blank(),
        axis.line = element_blank(),
  )
plt2 <-  tableGrob(cm_st)
grid.arrange(plt1, plt2, nrow = 1, ncol = 2,
            top=textGrob("Confusion Matrix",gp=gpar(fontsize=25,font=1)))

Conclusion

  • Predictive Model with 88% Accuracy.
  • Range was the strongest predictor of extinction.
    • Cape Floristic region (Fynbos biome)
    • Perennial shrubs
  • Habitat loss was the 2nd most important variable.
  • Further studies could include increased surveillance of threats, species monitoring, and ecological value of plant biodiversity.